MM or MI Cartridge?

Well said, @lewm .

Forgot also to mention typical compliance numbers that might affect response time. MCs typically exhibit lowest compliance. The exceptional MCs that exhibit higher than average compliance are the ones I like best.

The big difference between MC/MI/and MM cartridges boils down to a very few factors, most notably stylus profile, of which much ink has been spilled, and inductance, which is rarely mentioned. Moving coil carts have the lowest, then Moving Iron, and then Moving Magnet. why does this matter? Inductance directly relates to a property called hysteresis, the delay between a change in input and a change in output. Google 'hysteresis curve' and you'll see the characteristic 'S' shaped hysteresis curve, and its return, the hysteresis loop. Ultra low output MCs sound fast and detailed in large because they have low inductance, thus low hysteresis. MI carts like Grado and Soundsmith  have greater inductance, roughly in the 50mH range, but the difference is incremental. Most Moving Magnet carts have 10X more inductance around 450-550 mH and accordingly 10X more hysteresis, more delay between changes in input (stylus motion) and a change in output voltage. They simply cannot respond without 'smearing'. The tradeoff in general is output voltage, where MM carts win by a mile, thus making preamp design easier and more forgiving. This is why most MC carts require an additional level of gain, and usually worse S/N ratios. There are other factors, to be sure, vibration control, compliance, tracking ability, and several more but all of those can be controlled independently of the electromagnetic performance of the generator which is determined in large by the cartridge designers choice of MC, MI, or MM. I haven't gone into cartridge loading which is important, but cannot compensate for the hysteresis inherent in the design.
 

Bunch of ill thought out hooey here!

Hysteresis refers to the coil core material ONLY. There is no hysteresis in an air core coil, or a non-magnetic core material, such as aluminum or plastic. Iron alloy *can* have hysteresis, depending on the alloy or physical form. Hysteresis results in loss of magnetic flux, but no loss in speed, as magnetic flux is transferred at the same speed of light as do electrons travel through a conductor. Resistance to electrical flow or magnetic flux may decrease energy transfer, but NEVER speed! You need to go back and study EE 101! 
 

Laminated coil core materials exhibit very little hysteresis, as used in the Shure M24, V15-III, IV, V. 
 

MI cartridges, as a subset of MM, have wide ranging inductances, as do MM carts. There is no “set” range of inductances just because a cart is MI, or MM. To say there is, displays a complete ignorance of cartridge types and design over the last 7 decades. Inductance of MM/MI carts determines output using a given magnetic flux density. Cartridge loading affects FR of a given combination of inductance and magnetic field strength. 
 

MC, or MI/MM just categorizes which comprises you choose to accept. There is no inherent superiority. Whichever you choose, choose wisely. There are so-so MC carts, and also MI and MM carts. Don’t use a broad brush, using a bad example of an MC to condemn MCs, or condemn all MMs or MI carts because you had a so-so example.

Wolfie, Good point about the relationship between hysteresis and core material, or lack of same. But to my observation, the three types do group well apart from each other if you base it on inductance. LOMCs are always much less than 100uH (micro-Henries). Many are actually down in the 10uH and below range. Whereas MI types typically measure in the low mH range, and a classic MM will measure 400mH and higher. The difference between 10uH (for a LOMC with low internal R) and 500mH (for a classic MM) is 50,000X! But I still stand by my reasoning (see above) and my listening experience that leads me to believe the difference in inductance does not make LOMCs inherently superior to MI and MM types.  So, you and I agree on the end point.

I feel privileged and fortunate to have a Grado Epoch3 MI cartridge.

It instantly replaced my, highly regarded, Lyra Atlas SL.

By that I mean it did not “cream” the Lyra, but it greatly surpassed it in, the always vital and central, musicality. Most important to me, voices sound more natural.

I bought the Grado because I was curious about MI. Everything I read about the, somewhat legendary, MI Decca London Reference made me long for that kind of sound. But the Decca  turned out to be out of production. And those who own them seem to hold on to them tightly. And I don’t think there is anyone who rebuilds them. I may be wrong about that.

MM (MI) or MC? One can’t generalize. But, surely, there are now outstanding cartridges of all types.